Calculation of branching fraction and $CP$ violation in $B^{-}\to D_s^{-}{D}^0$ decay

The most precise measurement of the $CP$ asymmetry in the decay $B^{-}\to D_s^{-}{D}^0$ has been reported by LHCb collaboration with the value of $(-0.4\pm 0.5\pm 0.5)\mathrm{\%}$. In this study, the $CP$ violation in the decay $B^{-}\to D_s^{-}{D}^0$ has been calculated under the factorization approach. This decay mode includes current-current tree and penguin diagrams and their amplitudes are considered separately. In each of the tree and penguin amplitudes, the strong and weak phases have been introduced. The $CP$ asymmetry has been calculated in this work to be $(-0.35\pm 0.03)\mathrm{\%}$. Finally, from the sum of the amplitudes, we have calculated the total amplitude and obtained comparable results with experimental value for the branching ratio of $B^{-}\to D_s^{-}{D}^0$ decay.